How do I fill an area with vertices lined up in a grid over a complex surface?
Bridge egde loops and/or F2 addon can do the job here. But i dont think any tool can automatically do it all in "one click" for you here.

Bridge edge loops : select two opposite edges parts (with same accound of vertices in each) then ctrl+E and validate "bridge edge loops" :


F2 is an addon to easily make faces (mesh_f2.py). A tutorial and download link here : 

https://www.youtube.com/watch?v=ImSNOuvkKsw

https://wiki.blender.org/index.php/Extensions:2.6/Py/Scripts/Modeling/F2